Abstract
I thank Domenico Senato and his fellow organizers for the kind invitation to participate in this gathering of friends of Gian-Carlo Rota — to grieve with you his passing and to search with you for a renewal of the work he laid out for us. Mimmo and Elvira have asked me to speak about Gian-Carlo’s mathematical work — and I do so in keen recollection of the happy evenings the four of us spent together at a café on the corso in Cortona just in the summer of 1998. Gian-Carlo had a way of creating order in his life, imposing patterns on time so as to be able to concentrate his energies, and to plan for discussions with innumerable people. I like to compare this practice with the establishment of rules in the monastic orders. That summer’s Regola Cortoniense starts, as usual, not with the angelus but with lunch (no pasta, but with a big bowl of fruit to take to his room in prospect of an evening and morning without supplies). Then the combinatorial seminars, followed by a carefully scheduled series of tête-àtêtes with individual students and visitors. At 17h30 sharp, we climb into la Macchina Senato, for the short drive uphill from the Palazzone to the town. There, always at that table just outside the door of his favorite café, Gian-Carlo orders his evening meal: three scoops of gelato al cioccolato covered with a rich chocolate sauce, topped off with those tiny but ubiquitous Japanese parasols, which are promptly distributed as offerings. Discussion begins immediately on the umbral calculus, and lasts until after dark. A few pleasantries off the subject, to relax in the evening calm, and Mimmo and Elvira head for their lodging. Gian-Carlo and I return on foot (downhill) to the Palazzone. The day is complete. These were such happy hours for us all.
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References
Anick, D., Rota, G.-C. (1991): Higher order syzygies for the bracket algebra and for the ring of coordinates of the Grassmannian. Proc. Nat. Acad. Sci. USA 88, 8087–8090
Brini, A., Huang, R.Q., Teolis, A.G.B (1992): The umbral symbolic method for supersymmetric tensors. Adv. Math. 96, 123–193
Brini, A., Regonati, F., Teolis, A.G.B. (1999): Multilinear algebra over supersymmetric rings. Adv. Math. 145, 98–158
Chan, W., Rota, G.-C., Stein, J. (1995): The power of positive thinking. In: White, N.L. (ed.) Invariant Methods in Discrete and Computational Geometry. Kluwer, Dordrecht, pp. 1–36
Chan, W. (1998): Classification of trivectors in 6D-space. In: Sagan, B.E., Stanley, R.P. (eds.) Mathematical Essays in Honor of Gian-Carlo Rota. Birkhäuser Boston, Boston, MA, pp. 63–110
Grosshans, F.D., Rota, G.-C., Stein, J. (1987): Invariant theory and superalgebras. (CBMS Regional Conference Series in Mathematics, 69). American Mathematical Society, Providence, RI
Huang, R.Q. (1990): Combinatorial methods in invariant theory. Ph.D. Thesis, Massachusetts Institute of Technology
Huang, R.Q. (1990): Invariants of sets of linear varieties. Proc. Nat. Acad. Sci. U.S.A 87, 4557–4560
Huang, R.Q. (1991): Invariants of sets of lines in projective 3-space. J. Algebra 143, 208–218
Huang, R.Q., Rota, G.-C. (1994): On the relations of various conjectures on Latin squares and straightening coefficients. Discrete Math. 128, 225–236
Howe, R., Huang, R.Q. (1996): Projective invariants of four subspaces. Adv. Math. 118, 295–336
Klain, D.A., Rota, G.-C. (1997): Introduction to geometric probability. (Lezioni Lincei), Cambridge University Press, Cambridge
Kung, J.P.S. (ed.) (1995): Gian-Carlo Rota on Combinatorics. Birkhäuser Boston, Boston, MA
Metropolis, N., Nicoletti, G., Rota, G.-C. (1981): A new class of symmetric functions. In: Mathematical Analysis and Applications. Part B. Academic Press, New York, pp. 563–575
Rota, G.-C., Mullin, R. (1970): On the foundations of combinatorial theory: III. Theory of binomial enumeration. In: Harris, B. (ed.) Graph Theory and its Applications. Academic Press, New York. pp. 167–213
Rota, G.-C. (1973): The valuation ring of a distributive lattice. In: Faitlowicz, S., Kaiser, K. (eds.) Proceedings of the University of Houston Lattice Theory Conference. Department of Mathematics, University of Houston, Houston, TX, pp. 574–632
Rota, G.-C., Stein, J.A. (1990): Supersymmetric Hilbert space. Proc. Nat. Acad. Sci. USA 87, 653–657
Rota, G.-C. (1997): The many lives of lattice theory. Notices Amer. Math. Soc. 44, 1440–1445
Rota, G.-C. (1997): Indiscrete thoughts. Birkhäuser Boston, Boston, MA
Rota, G.-C. (1998): Introduction to geometric probability. (AMS Colloquium Lectures, Baltimore, January 1998) American Mathematical Society, Providence, RI, videocasette; edited version: Math. Intelligencer 20(4), 11–16
Rota, G.-C. (1998): Invariant theory, old and new. (AMS Colloquium Lectures, Baltimore, January 1998); edited version: Math Intelligencer 21(1), 20–27
Rota, G.-C. (2001): Twelve problems in probability no one likes to bring up. In: Crapo, H. Senato, D. (eds.) Algebraic combinatorics and computer science. A tribute to Gian-Carlo Rota. Springer Milan, pp. 57
Schanuel, S.H. (1986): What is the length of a potato? An introduction to geometric measure theory. In: Lawrence, F.W., Schanuel, S.H. (eds.) Categories in Continuum Physics. (Lecture Notes in Mathematics, (vol. 1174) Springer, Berlin, pp. 118–126 Blank
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Crapo, H. (2001). Ten abandoned gold mines. In: Crapo, H., Senato, D. (eds) Algebraic Combinatorics and Computer Science. Springer, Milano. https://doi.org/10.1007/978-88-470-2107-5_1
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DOI: https://doi.org/10.1007/978-88-470-2107-5_1
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